Characterization of Focused Seepage Through anEarthfill Dam Using Geoelectrical Methodsby S. J. Ikard1, A. Revil2,3, M. Schmutz4, M. Karaoulis5, A. Jardani6, and M. Mooney7
AbstractResistivity and self-potential tomography can be used to investigate anomalous seepage inside heterogeneous
earthen dams. The self-potential (SP) signals provide a unique signature to groundwater flow because the sourcecurrent density responsible for the SP signals is proportional to the Darcy velocity. The distribution of the SPsignals is also influenced by the distribution of the resistivity; therefore, resistivity and SP need to be used inconcert to elucidate groundwater flow pathways. In this study, a survey is conducted at a small earthen damin Colorado where anomalous seepage is observed on the downstream face at the dam toe. The data reveal SP anddirect current resistivity anomalies that are used to delineate three anomalous seepage zones within the dam and toestimate the source of the localized seepage discharge. The SP data are inverted in two dimensions using theresistivity distribution to determine the distribution of the Darcy velocity responsible for the observed seepage.The inverted Darcy velocity agrees with an estimation of the Darcy velocity from the hydraulic conductivityobtained from a slug test and the observed head gradient.
IntroductionEarthen dams are designed to allow a limited amount
of uniform seepage through their cores and foundations.When seepage exceeds than what is permitted, internalerosion may occur and increase locally the permeabilityof preferential flowpaths. As the permeability is increasedthrough erosion of finer particles, the hydraulics ofseepage zones will also change over time. This can
1Department of Geophysics, Colorado School of Mines, GreenCenter, Golden, CO; [email protected]
2ISTerre, CNRS, UMR CNRS 5275, Universite de Savoie, LeBourget du Lac, France.
3Corresponding author: Department of Geophysics, ColoradoSchool of Mines, Green Center, Golden, CO; [email protected]
lead to the formation of piping through the dam andthe development of subsurface voids, both of which cancause sinkholes on the crest or side-slopes (Fell et al.2003; Bendahmane et al. 2008). The occurrence of suchlocalized seepages zones may therefore result in thesudden failure of an earthen dam (Foster et al. 2002;Fell et al. 2003). These processes are responsible for thesecond cause of catastrophic failures for earthen dams, forabout 46 % of all documented failures (Foster et al. 2000,2002; Fell et al. 2003; Wan and Fell 2004).
The highly uncertain outcomes and timescales overwhich seepage zones can evolve to threaten the safetycondition of an earthen dam mandate a need for improvedmethodologies that allow for (1) noninvasive detectioncapabilities with improved resolution over broad andcompact spatial scales, (2) rapid deployment and detectioncapabilities so that the geometrical evolution of seepagezones can be monitored in real time, and (3) theability to provide quantitative estimates of seepage-relatedhydraulic parameters in real time with improved accuracy.
Our goal in this study is to take advantage of somerecent developments in self-potential tomography (SPT)(Soueid Ahmed et al. 2013), in order to detect preferentialflowpaths in earthen dams. The self-potential (SP) method
NGWA.org Groundwater 1
is a passive geophysical method sensitive to groundwaterflow (Sill 1983; Rozycki et al. 2006; Boleve et al. 2009,2011). Indeed, the source current density responsible forthe occurrence of SP signals is directly proportional to theDarcy velocity. However, the subsurface distribution ofelectric resistivity must also be known in order to interpretSP signals (Jardani et al. 2007). To our knowledge,SP and resistivity data are rarely used in concert tolocalized concentrated seepage in earth dams. In thisstudy, we apply the SP and direct current (DC) resistivitymethods to a small leaking earthen dam in Coloradoat which focused seepage has been observed on thedownstream toe.
Description of the Geophysical Methods
Electrical Resistivity TomographyDC resistivity method is an active geophysical
method that employs specific geometrical configurationsof electrode arrays to inject very low-frequency currentsinto the subsurface and measure a voltage drop responseat a set of electrodes. The ratio of the measured voltagedrop by the imposed electrical current, corrected forthe geometry of the array, corresponds to an apparentresistivity. A pseudosection corresponds to a collection ofapparent resistivity measurements (Griffiths and Barker1993). The pseudosection can be inverted in either twodimensions (2D) or three dimensions (3D) to producean electrical resistivity tomogram (e.g., Loke and Barker1996) that displays an estimate of the true subsurfaceresistivity distribution. This approach is called electricalresistivity tomography (ERT) and has been broadly usedin hydrogeophysics.
The inverse of the resistivity, the electrical con-ductivity, is related to two fundamental properties ofthe porous soils and rocks, namely the connectedporosity φ and the cation exchange capacity CEC(Revil 2013a, 2013b):
σ = 1
Fσw + σS (1)
σS ≈(
1
Fφ
)ρSβ(+) (1 − f ) CEC (2)
where σ w (in S/m) corresponds to the pore water con-ductivity, σ S (in S/m) denotes the electrical conductivityassociated with the electromigration of the cations inthe diffuse layer coating the surface of the grains (seeFigure 1a and 1b), F (dimensionless) is the formationfactor related to the porosity by Archie’s law (F = φ− m ,Archie 1942, m is called the cementation exponent orfirst Archie exponent and is typically in the 1.5 to 2.5range), ρS (in kg/m) denotes the mass density of the solidphase (typically 2650 kg/m3 for silicates), β(+) (m2/s/V)corresponds to the mobility of the counterions in thediffuse layer, the external part of the electrical dou-ble layer (see Figure 1b) (β(+)(Na+, 25◦C) = 5.2×10−8
m2/s/V), f (≈0.90) denotes the fraction of counterionsin the Stern layer (the inner part of the electrical dou-ble layer), and CEC denotes the CEC (in C/kg) of thematerial.
The ERT method has been extensively used on damsto determine the subsurface architecture of earthen damsand to perform monitoring of changes in porosity (Nasser1994; Panthulu et al. 2001; Cho and Yoem 2007; Sjodahlet al. 2006; Blome et al. 2011). An electrically conductivepathway can be conductive because of the high porosityof the material or because of the presence of clay witha high CEC and therefore a low permeability (Revil andCathles 1999). Therefore, ERT is sensitive to the presenceof conductive pore fluids but is not a flow indicator,and therefore, any interpretation should be carefullyanalyzed and informed with additional geophysical andhydraulic data. As discussed in the following section,the SP method is naturally a complementary methodto ERT.
The SP MethodThe SP method is a passive geophysical technique
directly sensitive to groundwater flow (e.g., Ikard et al.2012; Revil et al. 2012). It has been extensively usedqualitatively to investigate preferential groundwater flowpathways in dams and embankments (Ogilvy et al. 1969;Corwin 1985; Butler et al. 1989; Butler et al. 1990;Alsaigh et al. 1994; Panthulu et al. 2001; Minsley et al.2011) and more recently quantitatively (Boleve et al.2007a, 2009, 2011; Moore et al. 2011; Boleve et al.2012). Recent algorithms have been indeed developedto invert SP data in order to localize preferentialflowpaths using cross-correlation (Rozycki et al. 2006)and stochastic methods (Ikard et al. 2012) and to estimatethe groundwater flow pattern and Darcy velocity usingdeterministic inversion algorithms (Boleve et al. 2009,2011).
A SP mapping survey is simple to perform andrequires only a voltmeter characterized by a high internalimpedance (>10 M�), a cable reel, and two nonpolariz-ing electrodes to passively measure naturally occurringvoltages.
The occurrence of SP signals associated with ground-water flow originates at the pore scale. The pore waterinside of a porous material is never electrically neutral.There is usually an excess of charge in order to com-pensate for the deficiency of electrical charges on themineral surface at the pore walls (Overbeek 1952, seeFigures 1a and 1b). The flow of the pore water is respon-sible for the advective drag of this excess of electricalcharges (Figure 1c). This advective current density (flowof charges per unit surface area of a cross section of theporous material and per unit time) is called the stream-ing current density in the literature (Overbeek 1952; Sill1983; Levenston et al. 1999).
Revil and colleagues developed a new formulation ofthe streaming current density that is valid for any poresize (Jardani et al. 2007; Revil and Mahardika 2013). Inthis formulation, the source current density is associated
2 S. J. Ikard et al. Groundwater NGWA.org
L
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zrO
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o-Plane d-Plane
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M+
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Sketch of a charged capillary
Sketch of the electrical double layer Source current density
Mineral
Mineral
Pore
MineralFlow
(a)
(b) (c)
Figure 1. Description of the electrical double layer and the streaming current density. (a) Sketch of a single capillary ofradius R coated by the electrical double layer. (b) Sketch of the electrical double layer showing the Stern layer of sorbedcounterions and the diffusion layer; M+ denotes the metal cations while A− denotes the anions. The charge of the diffuse andStern layer counterbalances the charge on the mineral surface. A consequence of the electrical double layer is the existenceof an excess of electrical charge in the pore water, located in the vicinity of the mineral surface. The o-plane refers to themineral surface and the d -plane to the interface between the Stern layer and the diffuse layer. (c) The flow of water throughthe pore network drags this excess of charge generating a streaming current density (modified from Revil et al. 2011).
with the drag of the effective excess of charge QV causedby the flow of the pore water and is therefore given by
jS = QVu (3)
where u (in m/s) denotes the Darcy velocity and QV
(in C/m3) denotes the excess of electrical charge that iscarried along with the flow of the pore water. For pHcomprised between 5 and 8, Jardani et al. (2007) foundthat the QV is controlled by the permeability k (in m2)and they developed the following empirical relationship:
log10 QV = −9.2 − 0.82 log10 k. (4)
Equation 4 holds for a broad range of porous rocksand soils (see also an updated data set in Revil andMahardika 2013).
In conductive materials, the source current densityjS is responsible for an electrical field and the tangen-tial component of this electrical field is measured at
the ground surface (e.g., Revil et al. 2012). A classicalmistake is to mix the local potentials in the elec-trical double layer coating the surface of the grainswith the macroscopic field that is measured in SPstudies. These physical quantities are unrelated to oneanother.
With respect to the macroscopic electrical field, thegeneralized Ohm’s law for the total current density j iswritten as
j = σE + jS (5)
where σ denotes the electrical conductivity of the porousmaterial. Equation 5 is combined with a conservationequation for the electrical charge that is written as (Sill1983)
∇· j = 0 (6)
The combination of Equations. 5 and 6 yields thefollowing elliptic partial differential equation for the
NGWA.org S. J. Ikard et al. Groundwater 3
SP ϕ (in V) (Sill 1983):
∇· (σ∇ϕ) = ∇· jS (7)
The right-hand side of Equation 7 corresponds tothe SP source term associated with the Darcy velocitydistribution and the heterogeneity in the distribution ofthe volumetric charge density.
In terms of laboratory measurements, the magnitudeof the SP signals can be estimated from the streamingpotential coupling coefficient. This coefficient is quanti-fied as follows. We first express Darcy’s law in a saturatedporous media as u = − K∇h , where h (m) denotes thehydraulic head and K (m/s) the hydraulic conductivity(Darcy 1856). The streaming potential coupling coeffi-cient C (in V/m) is defined as the variation of the SPϕ for a variation of the hydraulic head h when flow isallowed through a core sample and the end-faces are notshort-circuited. C is given by
C ≡(
∂ϕ
∂h
)j=0
= −QVKρ (8)
where ρ = 1/σ denotes the electrical resistivity of theporous material (in � m). We will see in the followinghow this coefficient can be measured in the laboratory(Boleve et al. 2007b; Malama and Revil 2013).
Forward modeling of the SP signals associated withgroundwater flow was pioneered by Sill (1983). Figure 2shows the 2D forward modeling of the SP signalsassociated with the existence of a preferential seepagein an earthen dam (hydraulic conductivity K = 10−6 m/s)with granular sand-silt materials (K = 10−5 m/s) andwith a clay core (K = 10−9 m/s). We see the presenceof a negative anomaly upstream and the presence ofa positive anomaly downstream at the dam toe. Theamplitude of these SP anomalies is controlled both bythe conductivity of the pore water (fresh water implieshigher SP anomalies) and by the head gradient. Wepropose the use of SPT, a method recently proposedinitially by Jardani et al. (2007), to use SP signals todetermine the flowpath of an observed seepage in a smalldam in Colorado. The algorithm that will be used forthe inversion of the SP data is described in the nextsection.
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
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2 mV
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7 mV4 mV
-1 mV
-4 mV
Flow path
Distance (m)
Figure 2. Example of SP modeling on an earthen dam with a clay core. We have created a flowpath with an increasedpermeability channeling water through the clay core. The groundwater flow is used to simulate the SP signals. The SP signalsare collected at the ground surface to create the SP profile (adapted from Boleve et al. 2009). Note that the position ofthe positive SP anomaly coincides with the seepage area. Computation performed with the finite-element package ComsolMultiphysics 3.5.
4 S. J. Ikard et al. Groundwater NGWA.org
Self-Potential TomographyWith the finite-element method, Equation 7 can be
written in matrix form as (Soueid Ahmed et al. 2013)
dp = Km (9)
where dp represents the predicted SP data at a setof stations, m represents the vector of current density(for each cell and in 2D, the current density has twocomponents), and K is called the kernel and correspondsto the Green’s functions of the problem, which accountsfor the resistivity distribution. An extensive discussionabout the computation of the kernel for the source currentdensity is given by Jardani et al. (2008), and morerecently, a free software has been developed by SoueidAhmed et al. (2013). An important point is that the kernelcannot be computed correctly without the knowledge ofthe resistivity distribution. Therefore, ERT is an importantingredient of SPT.
The inversion of the SP signal recorded at theground surface involves a reconstruction of the spatialdistribution of the amplitude and direction of the sourcecurrent density vector m given a set of observed data do
(N -vector of observed SP data). Deterministic inversionwith Tikhonov regularization is used, considering theminimization of an objective function, which is the sum ofat least two terms. The first term is the data misfit functionfor which the difference (according to a given norm,usually the L2 norm) between the predicted and observeddata should be minimized. However, for potential fieldproblems, the solution of the inverse problem is highlynonunique and many models can reproduce the dataequally well. Therefore, a regularizer is added to the costfunction. The idea is to use a groundwater flow model (setup with a minimum of constraints, for example, flow ina homogeneous material with the correct topography andthe correct boundary conditions) as prior model (denotedas m0). The idea is to start the inversion from this modeland to perturb iteratively this prior model using the SPdata as additional constraints.
The objective function to minimize, Pλ(m), isdefined as
P λ (m) = ‖Wd (Km − do)‖22 + λ2 ‖W m (m − m0)‖2
2(10)
where do denotes the vector of observed SP data, thesubscript 2 corresponds to the L2 norm, λ the regular-ization parameter that is incorporated with the constraint0 < λ < ∞, and m = (
Jxs , Jz
s
)corresponds to the model
vector with the two components of the source currentdensity (x and z components). The model vector has there-fore 2M components (M is the number of cells used todiscretize the subsurface) and the kernel matrix K hasN × 2M components Kij =
(Kx
ij ,Kzij
).
In Equation 10, the matrix Wd = diag{1/ε1, . . . , 1/εN }denotes a diagonal weighting square (N × N ) matrix.Elements along the diagonal of Wd correspond to thereciprocal of the standard deviation squared. The matrix
W m = σ 2mI denotes the weighting diagonal matrix that
represents the weight of the a priori model used in theminimization controlled iteratively from the regularizationparameter.
The minimization of the objective function∂Pλ(m)/∂m = 0 is conducted with the Gauss-Newtonalgorithm implemented in Matlab (see Richards et al.2010 and Soueid Ahmed et al. 2013). The program wasinitiated with a prior model and λ = 1, which reduces ateach iteration to half of the value at the previous iteration.After the third iteration, the SP data are reproduced with asmall RMS error of 0.12%. The current density vector istranslated into Darcy velocity using the linear relationshipbetween current density and Darcy velocity u = jS/QV
for the value of QV that determined from laboratory teststo quantify the coupling coefficient.
Description of the Test Site
Localization and GeometryThe field site is an earthfill dam (no clay core;
properties described in next section) that impounds a smallreservoir in the Rocky Mountains near Avon, Colorado.The reservoir is flanked by the steep, brushy sub-alpineside-slopes of the drainage gulch and collects surfaceand groundwater from a 7.8 km2 drainage basin. It hasa normal storage capacity of 24,670 m3. The reservoirsurface area is approximately 8094 m2 at the maximumstorage elevation of 2411 masl (meters above sea level),and the maximum reservoir depth is 5.8 m at full capacity.The dam has a structural height of 11 m (referenced tothe downstream dam toe), a hydraulic height of 10 m,and 1 m of freeboard elevation between the emergencyspillway S1 and embankment crest at the maximumpool elevation (Figure 3b). The dam is 37 m wide atthe base and is 4.9 m wide at the crest. The crestis at an elevation of 2412 masl and spans 122 m inlength between the side-slopes of the drainage gulch.The upstream slope of the embankment is lined with rip-rap on a 2:1 slope (horizontal:vertical) to an elevationof 2409 masl and has 3:1 grade below. The downstreamslope has a 2:1 grade to the toe at 2402 masl, wherethe downstream slope intersects the natural topographyof the gulch. Portions of the downstream slope near thetoe of the maximum cross section are significantly steeper(as much as 1.6:1).
The dam has two spillways. The primary spillway(see Spillway S1 in Figure 3b) is a 630-mm diametercorrugated metallic pipe through the west abutment intothe reservoir. We have checked that the corrugatedmetallic pipe is responsible for a small negative SPanomaly that does not influence the overall SP mapdiscussed later. The emergency spillway (shown inFigure 3b as Spillway S2) on the east abutment is anopen channel graded from 9 m wide at the concrete cutoffwall marking the spillway crest into a 3.7-m wide channel,approximately 26 m downstream.
NGWA.org S. J. Ikard et al. Groundwater 5
Crest Reservoir at low level
Spillway S1
Reservoir water gauge
Picture of the test site
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P1 1
P10 P8P7
P6
P12 P9
P1
Position of the profiles(a)
(b)
Pz1
Spillway S2
S2
S1
Figure 3. Description of the test site. (a) Position of the DCresistivity and SP profiles for the reconnaissance survey. FiveDC resistivity profiles (P1 to P5) were acquired parallel tothe dam crest with a 2.5-m electrode spacing, and six profiles(P6, P7, P8, and P10 to P12) were acquired perpendicular tothe dam crest with a 1-m electrode spacing. One profile (P9)was collected oblique to the East abutment, perpendicularto a suspected seepage path through the abutment, witha 1-m electrode spacing. A total of 1049 SP stations wereacquired along DC survey lines with a 1.25-m spacingparallel to the crest and a 1-m spacing perpendicular to thecrest (Ref. denotes the position of the reference for the SPmeasurements). (b) Picture of the reservoir lake at low levelwith the position of the two spillways S1 and S2 and thecrest of the earth dam. The overflow pipe is also visible inthe middle of the dam (see “Reservoir water gauge”).
Properties of the Dam MaterialsGeotechnical properties and internal zoning of the
dam are unknown. The few available inspection recordsand engineering reports (Blair 2003, 2004, 2010a, 2010b)have assumed that the dam is composed of homogeneousearthfill resembling soils encountered in test pits exca-vated at the east abutment of the dam, due to the closeproximity of the test pits to original 1936 borrow area. TheState of Colorado assumes that the dam is homogeneousearthfill composed of silty clay materials compacted to95% maximum density during emplacement (Blair 2003,2004, 2010a, 2010b), but this is unconfirmed. Quantita-tive geotechnical data regarding the original constructionmaterials and those used in historical modifications arenot available.
Anomalous SeepA seep has been observed at the downstream toe
of the maximum cross section of the dam (see “seeparea” in Figure 4). During this study, visible water exitingthe dam at the downstream toe (i.e., seep) was observedover a distance of few meters parallel to the dam crestapproximately intersecting resistivity line P6 (see positionin Figure 3a). The discharging seepage water flowscontinuously under the hydraulic load of the maximumreservoir storage behind the dam. Visual observationsrecorded by field engineers and state regulators on severaloccasions over a period of 2 years have indicated that theseepage exiting the downstream toe is between 0.6 L/s and1.9 L/s when the reservoir is at full capacity.
Data AcquisitionSP and DC resistivity surveys were completed in
summer 2011 to identify the source of anomalous seepageemanating from the dam toe. The reservoir water level washeld constant at the maximum storage level (2412 masl)throughout the survey. The seepage zone water wasobserved to be clear. The electrical conductivities of thereservoir water and seepage water were measured to be308 μS/cm and 440 μS/cm (at a temperature of 8.7oC),respectively, using a conductimeter.
Twelve DC resistivity profiles were collected paralleland perpendicular to the dam covering the crest, spillways,downstream slope, and a portion of the downstream topog-raphy and side-slopes of the drainage gulch (Figure 3a).Resistivity measurements were acquired with an ABEMTerrameter SAS4000 using a Wenner array with 64 elec-trode separated by 2.5 m for profiles parallel to the damcrest and separated by 1 m for profiles perpendicular tothe crest. The measured contact resistivity between theelectrodes and the ground was less than 1 k�. The resis-tivity measurements were repeated to achieve a standarddeviation of the apparent resistivity that was less than 3%of the mean value.
The resistivity profiles along the upstream edge (P1)and downstream edge (P3) of the crest were separatedby 5 m, and DC resistivity profiles on the downstreamslope parallel to the crest (P2, P4, P5) were separated byabout 10 m (Figure 3a). The profiles perpendicular to thecrest (P6 to P12) had an average separation of 16 m. Oneadditional profile (P9) was performed perpendicular to asuspected seepage path through the East abutment using59 electrode takeouts and an electrode separation of 1 m.
A total of 1049 SP stations were monitored along theDC resistivity profiles with a handheld Fluke 289 volt-meter and two nonpolarizing Petiau Pb-PbCl2 electrodes(Petiau 2000). A reference Petiau electrode was buriedin a shallow hole that was excavated above the reservoiron the east side-slope of the gulch (see position “Ref”in Figure 3a), and a roving Petiau electrode was used ateach of the 1049 stations. All SP data were measuredas the potential difference between the roving electrodeand the reference electrode. The station separation forSP measurements was 1.25 m for profiles parallel to the
6 S. J. Ikard et al. Groundwater NGWA.org
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Vadose zone
Figure 4. Example of 2D resistivity and SP profile normal to the dam structure (Profile P6, see position in Figure 1a). Thegrey area corresponds to the area where seepage A2 can be observed at the ground surface. This seepage is associated witha relative 20 mV positive SP anomaly with respect to the local minima on its flanks (surrounding values).
crest and 1 m for profiles perpendicular and oblique tothe crest. At each SP station, a shallow hole was exca-vated to expose moist soil and reduce contact resistancebetween the roving electrode and the ground. Stations onthe crest and some stations perpendicular to the west abut-ment were watered with reservoir water to reduce contactresistance. The maximum contact resistance for all SPstations was 40 k� and on average was less than 15 k�,much smaller than the internal impedance of the volt-meter (100 M�). The potential difference was measuredbetween the reference and roving Petiau electrodes beforeand after acquiring each 1049 station survey to correctfor electrode drift. Telluric currents were assumed to benegligible due to the small, confined nature of the fieldsite and were not monitored. Some SP profiles are shownin Figures 4 to 6 together with the resistivity profiles. ASP map is shown in Figure 7.
Electrical Resistivity Tomogram (ERT)The inversion of the apparent resistivity data was
performed with RES2DINV (Loke and Barker 1996)with the finite-element approach and a Gauss-Newtonalgorithm. The 2D DC resistivity profiles and the
associated SP data are shown in Figures 4 to 6. Dataquality was excellent due to a very good contact betweenthe stainless steel electrodes and the ground (contactresistance generally < 1 k� as discussed earlier).
Five profiles (P1 to P5) were also inverted in 3Dwith the software ERTLab (Morelli and Labrecque 1996,Santarato et al. 2011) using the finite-element methodwith tetrahedrons. The 3D inversion only incorporatedthe profiles collected parallel to the dam crest, theprofiles normal to the dam were spaced too far apartto bring pertinent information. The whole data set forthe 3D inversion was composed of 319 electrodes,2357 quadripoles, and 323 topographic data points. Theinversion converged in three iterations leading to a lowRMS error of 5%. The topography was taken into accountin the inversion. The mesh grid size was equal to 1.25 m inall directions. The result of the 3D tomography is shownin Figure 8.
Interpretation of the Geophysical DataThe resistivity profiles show a shallow resistive layer
(resistivity in the range 200 to 300 � m) just below theground surface, e.g., profile P6 in Figure 4. This layer
NGWA.org S. J. Ikard et al. Groundwater 7
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West East
Figure 5. Example of 2D resistivity and SP profile parallel to the dam crest (Profile P2). The high density of measurementcan be used to determine the standard deviation to be 3 mV. This profile shows the lateral zone of saturation associated withthe aquifer. The SP signals are essentially uniform indicating a rather uniform seepage in the upper part of the dam.
is interpreted as the vadose zone above the capillaryfringe. This is consistent with the fact that the water tableis approximately 1 to 2 m below the ground surface atpiezometer Pz1 (see position in Figure 3a).
The resistivity profiles show areas of low-resistivityanomalies (on the order of 40 to 50 � m, see Figures 4to 6 and Figure 8). The conductivity of the pore water isσ w = 0.052 S/m (19 � m resistivity, 529 μS/cm) measuredin the field in piezometer Pz2 on July 9, 2012 (onJuly 9, 2012, the background conductivity in piezometerPz1 was measured and was 549 μS/cm). The referencedvalues were 440 μS/cm and 308 μS/cm August 9, 2011during the reconnaissance survey. The porosity of thedam material is estimated to be around 0.30 (30%).This implies a formation factor F of about 11 (usinga cementation exponent of 2.0 as default value, seeArchie 1942). σ = 0.025 S/m (using 40 � m from theresistivity tomogram) implies a surface conductivity σ S
of 0.020 S/m. This is a rather high value indicating thatthe earth material could be clayey. We interpret the low-resistivity zones as areas of relatively high permeabilityand the value of the permeability will be discussed further.However, as mentioned earlier, great care should be takenin analyzing resistivity as it is influenced by the claycontent, the clay mineralogy, and porosity.
The low-resistivity area below the crest (see Figure 5)is interpreted as a seepage zone of the groundwater thathas entered the dam cross section from the reservoir.Beneath the crest, the phreatic surface is uniformlydistributed in Profile P2 (see Figure 5), suggesting auniform entry of reservoir water into the upstream slope ofthe dam. The seepage separates into preferential flowpathsin a downstream direction as shown in Profiles P2 and P5parallel to the crest (Figure 6). Seepage starts to deviatefrom uniform into preferential channels in Profile P4 (notshown here) along the midsection of the downstreamslope. In Profile P5 (Figure 6), we can clearly observethree localized channels in the dam shown by conductiveanomalies (see also Figure 8 where these seepages arenamed Paths 1, 2, and 3). Flow through the central pathappears to be the primary contribution to the observedseep at the downstream dam toe (see position of the seepin Figures 4 and 7). Indeed, the high-conductivity seepage“Path 2” correlates at its termination with the position ofthe observed seep.
SP data are complementary to the 2D/3D electricalresistivity tomograms in deciphering the position of theflowpaths. The positive SP anomalies (∼15 to 30 mVwith respect to the reference electrode) are observeddownstream of the dam, in its central portion (see the
8 S. J. Ikard et al. Groundwater NGWA.org
−20
−15
−10
−5
0
5
10
15
20
0 50 100 150
Profile P5
Self
-pot
entia
l (in
mV
)
September 2011
Iteration 4, RMS 5.1%
Dep
th (
in m
eter
s)
10
5
0
−5
−10
−15
−20
−25
−30
BedrockPath 2
Spillway S2Spillway S1
Resistivity (in ohm m)
40 50 70 100 200 300
A1
Path 1 Path 3
Green vegetation
Seep
Position (in m)West East
Figure 6. Example of 2D resistivity and SP profile parallel to the dam crest (Profile P5). The high density of measurementallows determining the value of the standard deviation (about 3 mV). This profile shows three well-developed flowpaths namedPath 1, Path 2, and Path 3. Path 2 is responsible for the observed seepage on the downstream toe of the dam. Its seepage isassociated with a positive SP anomaly with respect to the background value.
anomalies A1 and A2 in Figure 7). The maximumpositive SP anomaly was observed in Profile P6 (seeFigure 4). Note that both spillways were carryingwater during the survey. The positive SP anomalieson the downstream slope of the dam are interpretedas zones of water upwelling in the vicinity of theground surface (see for instance the simulation shown inFigure 2). The localization of these zones is consistentwith the position of the preferential flowpaths interpretedfrom the DC resistivity profiles. A clear seep is onlyobserved at the bottom of Profile P6 (see Figure 4).However, other indicators of seepage (for instance greenand abundant vegetation) have been observed at somelocations on the downstream slope that are consistentwith positive SP anomalies (>10 mV with respect tothe background, see for instance Figure 6). The locationof anomaly A1 in Figure 7 has been consistentlyobserved over several months to have significantly greenervegetation with respect to surroundings. This area wasnoted to show increased soil moisture content withrespect to surroundings and a “sloshing” sound whenDC electrodes were installed in this location. Tall,dense vegetation and noxious weeds have been observedsprouting from the downstream slope at the location of
A2 (Figure 7) during the summers of 2009 and 2010.A2 and A3 were also observed to have increased soilmoisture (although not as significant as A1) with respectto surroundings.
Self-Potential TomographyThe goal of this section is to show how the SP
data along Profile P6 can be interpreted quantitatively toestimate the Darcy velocity. For this purpose, we firstdetermine the streaming potential coupling coefficient ofa core sample from the dam and then we proceed to invertthe SP data in terms of source current density distribution,which is then converted into a spatial distribution of Darcyvelocity.
Laboratory InvestigationA sample of material representative of the aquifer
shown in Figure 4 has been collected at a depth of 2 mwith an auger. The sample was estimated to be predom-inantly silty clay through visual and textural analysis. Itwas representative of the texture and composition to theembankment fill materials described in the lithologic logs.The embankment fill materials is a disturbed version of
NGWA.org S. J. Ikard et al. Groundwater 9
Area 1
Area 2
Ele
vatio
n (m
)
2415
2410
2405
4388300
4388280
4388260
4388240
4388220
SeepA1A2A3
Self-potential map (with topography)(a)
(b)
Self
-pot
entia
l (in
mV
)
25
15
5
−5
−15
−25
Easting (m)372000
372020
372040
372060
372080
Northing (m)
Thresholded resistivity tomography
Seep
Seepage 1Seepage 2
Seepage 3
Area 1
Area 2
Figure 7. SP and resistivity data. (a) SP map (total of 1049 SP stations). Negative SP anomalies on the abutments anddownstream slope in the approximate range of −15 to −30 mV are a result of flow through preferential paths imaged inDC resistivity tomography. The positive SP anomalies in areas A1 to A3 may correspond to the upflow of water as shownin Figure 2. Anomaly A2 indicates the potential for upflow paths near the observed seepage zone. The areas A1 and A3 arecharacterized by very green vegetation. “Seep” corresponds to the position of the observed seep downstream the dam. (b)Threshold resistivity distribution showing the anomalies less than 50 �m in magnitude.
the soils excavated from on-site borrow areas, which havebeen reported to be silty clays, although no quantitativegeotechnical data are available to confirm this assump-tion. The silty clay assumption, as well as the texturalcharacteristics observed and recorded during the sampleexcavation, do justify the use of this high value. Thehydraulically conductive nature of the sediments indicatedby the slug test is in agreement with lithologic logs ofpiezometer installation. Boring logs for piezometers Pz1and Pz2 were supplied by Hepworth-Pawlak Geotech-nical. Borings were drilled on July 28, 2004 using atrack-mounted drill rig during a low pool storage conditionin the reservoir. Unfortunately, geotechnical analysis ofboring samples was not performed in a laboratory. Boringlogs of Pz1 indicate that embankment fill was encounteredbetween depths of 0 m and 11 m consisting of sandy grav-elly clay, scattered cobbles. The fill was medium stiff tovery stiff, moist, and dark brown in color. Gravel wasencountered below the embankment fill between depthsof 11 and 15 m. The gravel was noted to be dense, sandy,and silty with cobbles and small boulders and was redin color. It was also noted to be moist with saturation
increasing with depth. The water table was encounteredat a depth of 15 m in Pz1 during installation. Pz1 is slot-ted between depths of 11.5 and 15 m. The lithologic login Pz2 indicates that embankment fill was encounteredbetween depths of 0 m and 4.6 m and has the same char-acteristics as those encountered in Pz1. The gravel layerencountered in Pz1 was also encountered in Pz2 betweendepths of 4.6 and 8.6 m. The water table was encoun-tered at a depth of 5.3 m during installation. Pz2 is slottedbetween 5 and 8.6 m. The logs show a more hydraulicallyconductive layer underneath the embankment fill.
Our goal was to use this sample to get an estimate ofthe streaming potential coupling coefficient to connect thesource current density to the Darcy velocity. The experi-mental setup used is shown in Figure 9a and the streamingpotentials vs. hydraulic heads are shown in Figure 9b.Water from the reservoir was used for this experiment.The value of the streaming potential coupling coefficientis determined from the slope of the streaming potential vs.hydraulic head data, which is equal to −2.6 ± 0.2 mV/m.We also measured the resistivity (40 � m) and the perme-ability (k = 3.8 × 10−12 m2, corresponding to a hydraulic
10 S. J. Ikard et al. Groundwater NGWA.org
(a)
(b)
(c)
Figure 8. 3D electrical resistivity tomogram from ProfilesP1 to P5 (2357 apparent resistivity data). (a) 3D inversionof the DC resistivity. (b, c) 2D plan view slices at differentdepths below the topography. Three potential seepage pathsare shown within the dam, diverging from uniform flowin a downstream direction. One path is imaged througheach abutment, and one path is imaged beneath themaximum cross section in the center of the dam. The centralpreferential flowpath (Path #2) through the maximum crosssection of the dam appears to be the primary contributionof flow into the seepage zone (spring) observed in Profile P6(Figure 4) as well as in the field.
conductivity K = 3.7 × 10−5 m/s) of the soil sample.Substituting the value of the permeability into Equation 4,we obtain QV = 1.5 C/m3. Using Equation 8, the effec-tive charge per unit volume is given by QV = −C/ (Kρ).Using this formula with the measured parameters givenpreviously yields QV = 1.5 C/m3. The two estimatesare therefore very close to each other. The value ofQV = 1.5 C/m3will be used to convert the source currentdensity distribution into Darcy velocity. Using, however,a single value for QV while the dam is heterogeneous canonly yield a rough estimate of the Darcy velocity. Thiswill be discussed in the following section.
Inverting the SP FieldThe SP data from Profile P6 were inverted to
understand the seep observed in the field at location A2 inProfile P6 (see Figure 4). We consider N = 55 SP stationsalong Profile P6 and we use M = 103 cells to discretizethe subsurface as shown in Figure 10.
The prior model m0 used for the inversion of the SPdata is determined from a simulation of the groundwaterflow assuming the position of the bedrock/aquifer inter-face (from the resistivity data) and a uniform permeability
R2 = 0.98
Streaming potential coupling coefficient
C = −2.6 ± 0.2 mV m−1
0 0.2 0.4 0.6 0.8 1.0Hydraulic head (m)
Dif
fere
nce
of e
lect
rica
l pot
entia
l (m
V)
5
4
3
2
Water
RefV
Porous samplePermeable membrane
h
(a) (b)
Figure 9. Measurement of the streaming potential couplingcoefficient for a core sample from the dam. (a) Sketch ofthe experimental setup where h denotes the hydraulic head.(b) The measurements have been made with water fromthe reservoir. The value of the streaming potential couplingcoefficient is −2.6 ± 0.2 mV/m.
for the aquifer. We specify the boundary conditions for thehead at the top and bottom of the profile and the ground-water flow is modeled in steady state. For the matrix Wd,we use a standard deviation of ε=3 mV from the datadisplayed in Figures 4 to 6. For the matrix W m, we useσ 2
m=100 to let enough freedom to the inverted model todepart from the prior model m0.
A linear hydrostatic pressure head profile was com-puted and applied to the upstream slope to vary thehydraulic head applied to the model boundary based onrelative elevation of the boundary with respect to the highpool water level. A seepage face was defined at the down-stream toe where seepage has been observed, as H = 0 munder saturated conditions and a specified flux equal to0 m3/s otherwise. All other model boundaries were givena specified flux equal to 0 m3/s.
For the electrical model, a current flow boundary wasapplied to the reservoir bed, upstream slope of the dam,and the downstream seepage face. The current densities atthese boundaries were computed from the electrokineticequations that couple the electric field to the Darcyvelocity computed in the hydraulic model.
Modeling results are shown in Figure 10. Thecurrent density vector is translated into Darcy velocityusing the linear relationship between current density andDarcy velocity (see Equation 3) u = jS/QV using QV
= 1.5 C/m3. The results of the SPT are consistent withthe position of the bedrock (for which the Darcy velocityshould be very small). The two positive SP anomaliesare explained by the convergence of the flow due to thefact that the bedrock is shallower in the vicinity of theseanomalies. The seepage corresponding to the spring isshown very well by the inverted Darcy flow, showing ahigh Darcy velocity oriented partly upward at the positionof the SP anomaly.
A slug test performed in piezometer Pz1 indicatesthat the permeability of the formation is on the orderof 10−12 m2 (K = 10−5 m/s), which is a pretty large
NGWA.org S. J. Ikard et al. Groundwater 11
Horizontal distance (m)
0 10 20 30 40 50
Ground surface
Seepage
Crest
Bedrock
Dep
th (
m)
0
Δ
2
4
6
8
10
12
14
Darcy velocity from the self-potential data (P6)
Aquifer
Log10 (Darcy velocity, m/s)
−5.5 −5.0 −4.5 −4.0 −3.5
Fit of the self-potential data
−20
−10
0
10
20(a)
(b)
Self
-pot
entia
l (in
mV
)
Horizontal distance (m)
Data
Best fit
0 10 20 30 40 50
Pz1
Pz2
Figure 10. Result of the inversion of the SP data along Profile 6 and flow Path #2. (a) Best fit of the experimental data at thethird iteration of the Gauss-Newton algorithm. The standard deviation on the data is considered to be 3 mV from the scatterin the SP data. (b) Result of the Darcy velocity distribution assuming an excess of charge density of 1.5 C/m and the invertedsource current density obtained at the third iteration. The dashed line represents approximately the interface between thebedrock and the aquifer determined from the resistivity data. The white area between the water table and the ground surfacecorresponds to the vadose zone.
value. From the shape of the vadose zone shown inFigure 4, the head gradient is estimated to be on theorder of 0.33. Therefore, the Darcy velocity is about3 × 10-6 m/s in the vicinity of the piezometer Pz1. TheSP tomogram converted into Darcy velocity distribution(Figure 10) indicates a higher Darcy velocity on the orderof 3 × 10−5 m/s in this region so it is possible that theSP tomogram slightly overestimates the Darcy velocitypossibly because of the value of QV chosen previously.
ConclusionsA small earthen dam exhibiting concentrated internal
seepage and a visible seep at the toe was imaged using
DC resistivity and SP during an instance of maximumreservoir capacity and therefore peak hydraulic loading. Aseries of 2D resistivity profiles were inverted individuallyand combined for 3D inversion. SP data were collectedalong the resistivity profiles for comparison. The SP datawere inverted to estimate Darcy velocities. The followingconclusions have been reached:
1. Resistivity identifies three potential flowpaths; how-ever, resistivity is not a direct indicator of permeabilityand fluid flow.
2. SP can be directly tied to permeability and thesource current density responsible for the SP signalsis proportional to the Darcy velocity. However, the
12 S. J. Ikard et al. Groundwater NGWA.org
distribution of the SP signals is also controlled by theresistivity distribution.
3. We have proposed a SPT algorithm to image ground-water flow using the SP signals, collected at the groundsurface of the earth dam and using the resistivitydistribution to reconstruct approximately the distribu-tion of the Darcy velocity. We identified a flowpaththat agrees with an anomalous seepage observedon the downstream of the dam toe and we determinedthe distribution of the Darcy velocity.
AcknowledgmentsThis work was supported by the NSF-funded Smart-
Geo Educational Program (Project IGERT: IntelligentGeosystems; DGE-0801692) and the NSF-funded PIREproject. We thank Golder Associates, Inc., and Traer CreekLLC. for logistical support and site access and the threereferees for very constructive comments and the timespent on our manuscript.
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